Archimedes Principle and Buoyancy

A $200 \mathrm{g}$ solid block of Aluminium (Density of Al = $2.70 \mathrm{g}/\mathrm{cc}$) is placed in a beaker of water filled to the brim. Some water overflows. The same is done in another beaker with a $200 \mathrm{g}$ solid block of lead (Density of lead = $11.3 \mathrm{g}/\mathrm{cc}$). Does the block of lead displace more, less, or the same amount of water as the aluminium block?

A $200$ g solid block of Aluminium (Density of Al = $2.70$ g/cc) is placed in a beaker of water filled to the brim. Some water overflows. The same is done in another beaker with a $800$ g solid block of lead (Density of lead = $11.3$ g/cc). Does the block of lead displace more, less, or the same amount of water as the aluminium block?

Two cylinders of same cross-section area and length $L$ but made of two material of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with a length$\frac{L}{2}$above the surface of the liquid. If $d_1>d_2$, then

A cork of density $0.5 \mathrm{g} {\mathrm{cm}}^{-3}$ floats on a calm swimming pool. The fraction of the cork's volume which is under water is

A container of large surface area is filled with liquid of density $\text{ρ}$ . A cubical block of side edge a and mass M is floating in it with four-fifth of its volume submerged. If a coin of mass m is placed gently on the top surface of the block is just submerged. M is

Two bodies having volumes $V$ and $2V$ are suspended from the two arms of a common balance and they are found to balance each other. If larger body is immersed in oil (density $d_1=0.9 \mathrm{g} {\mathrm{cm}}^{-3}$) and the smaller body is immersed in an unknown liquid, then the balance remain in equilibrium. The density of unknown liquid is given by

A slender homogeneous rod of length 2L floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is 0.75. The length of rod that extends out of water is

A cuboidal piece of wood has dimensions a, b and c. Its relative density is d. It is floating in a large body of water such that side a is vertical. It is pushed down a bit and released. The time period of SHM executed by it is

Two cubes of size $1.0 \mathrm{m}$ sides, one of relative density $0.60$ and another of relative density $=1.15$ are connected by weightless wire and placed in a large tank of water. Under equilibrium the lighter cube will project above the water surface to a height of

Some liquid is filled in a cylindrical vessel of radius $R$. Let $F_1$_​ be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square cross-section of side $R$. Let $F_2$ be the force applied by the liquid on the bottom of this new vessel. Then

An expansible ballon filled with air floats on the surface of a lake with 2/3 of its volume submerged. How deep must it be sunk in the water so that it is just in equilibrium neither sinking further nor rising ? It is assumed that the temperature of the water is constant & that the height of the water barometer is 9 meters

In air an object weighs 15N, when immersed completely in water the same object weighs 12N. When immersed in another liquid completely, it weighs 13N. Find the specific gravity of the object.

Some iron beads are embedded in wax ball which is just floating in water. The volume of ball is $18\mathrm{ }\mathrm{c}{\mathrm{m}}^3$ and relative density of wax is $0.9$. Then mass of the iron trapped in the ball is 

If there were no gravity, which of the following will be not there for a fluid?

A hot air balloon is carrying some passengers, and a few sandbags of mass $1 \mathrm{kg}$ each so that its total mass is $480 \mathrm{kg}.$ Its effective volume giving the balloon its buoyancy is $V.$ The balloon is floating at an equilibrium height of $100 \mathrm{m}.$ When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to $150 \mathrm{m}$ with its volume $V$ remaining unchanged. If the variation of the density of air with height $\mathrm{h}$ from the ground is $\rho \left(\mathrm{h}\right)={\rho }_0{\mathrm{e}}^{-\frac{\mathrm{h}}{{\mathrm{h}}_0}},$ where ${\rho }_0=1.25 \mathrm{kg}{ \mathrm{m}}^{-3}$
and ${\mathrm{h}}_0=6000 \mathrm{m},$ the value of $\mathrm{N}$ is________.

A vessel contains two immiscible liquids of density ${\rho }_1=1000 \mathrm{kg}/{\mathrm{m}}^3$ and ${\rho }_2=1500 \mathrm{kg}/{\mathrm{m}}^3.$ A solid block of volume $V={10}^{-3} {\mathrm{m}}^3$ and density $d=800 \mathrm{kg}/{\mathrm{m}}^3$ is tied to the bottom of the vessel by a light string as shown. The block is immersed with ${\left(\frac{2}{5}\right)}^{\mathrm{th}}$ of its volume in the liquid of higher density and ${\left(\frac{3}{5}\right)}^{\mathrm{th}}$ in the liquid of lower density. The entire system is kept in an elevator which is moving upwards with acceleration $a=\frac{g}{2}$. Find the tension in the string in Newton $\left[g=10 \mathrm{m}/{\mathrm{s}}^2\right]$

A ball whose density is $0.4\times {10}^3\mathrm{kg} {\mathrm{m}}^{-3}$ falls into water from a height of $9 \mathrm{cm}$. The depth upto which the ball sinks is ____$\mathrm{cm}$.

If $w_1=$ weight of a body and $w_2=$ buoyant force exerted by the liquid on it, then the body will remain floating with some portion of it above the liquid surface when -

A piece of ice is tied using a string to the bottom of bucket $A$. The bucket is filled with water with ice completely submerged in it. Another bucket $B$ is filled with water and a piece of ice is released in water. If floats on the surface of water (see Fig.). What would be the impact on the level of water in the two buckets, when ice pieces melt away completely?

A metal sphere connected by a string is dipped in a liquid of density $\rho$ as shown in figure. The pressure at the bottom of the vessel will be,

$\left(p_0\right.$is atmospheric pressure$)$